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Parameter estimation in discrete or continuous deterministic cell cycle models is challenging for several reasons, including the nature of what can be observed, and the accuracy and quantity of those observations. The challenge is even greater for stochastic models, where the number of simulations and amount of empirical data must be even larger to obtain statistically valid parameter estimates. The two main contributions of this work are (1) stochastic model parameter estimation based on directly matching multivariate probability distributions, and (2) a new quasi-Newton algorithm class QNSTOP for stochastic optimization problems. QNSTOP directly uses the random objective function value samples rather than creating ensemble statistics. QNSTOP is used here to directly match empirical and simulated joint probability distributions rather than matching summary statistics. Results are given for a current state-of-the-art stochastic cell cycle model of budding yeast, whose predictions match well some summary statistics and one-dimensional distributions from empirical data, but do not match well the empirical joint distributions. The nature of the mismatch provides insight into the weakness in the stochastic model.

Significant effort has been devoted to designing clustering algorithms that are responsive to user feedback or that incorporate prior domain knowledge in the form of constraints. However, users desire more expressive forms of interaction to influence clustering outcomes. In our experiences working with diverse application scientists, we have identified an interaction style scatter/gather clustering that helps users iteratively restructure clustering results to meet their expectations. As the names indicate, scatter and gather are dual primitives that describe whether clusters in a current segmentation should be broken up further or, alternatively, brought back together. By combining scatter and gather operations in a single step, we support very expressive dynamic restructurings of data. Scatter/gather clustering is implemented using a nonlinear optimization framework that achieves both locality of clusters and satisfaction of user-supplied constraints. We illustrate the use of our scatter/gather clustering approach in a visual analytic application to study baffle shapes in the bat biosonar (ears and nose) system. We demonstrate how domain experts are adept at supplying scatter/gather constraints, and how our framework incorporates these constraints effectively without requiring numerous instance-level constraints.

Hidden Markov model (HMM) classifier design is considered for the analysis of sequential data, incorporating both labeled and unlabeled data for training; the balance between the use of labeled and unlabeled data is controlled by an allocation parameter \lambda \in [0, 1), where \lambda = 0 corresponds to purely supervised HMM learning (based only on the labeled data) and \lambda = 1 corresponds to unsupervised HMM-based clustering (based only on the unlabeled data). The associated estimation problem can typically be reduced to solving a set of fixed-point equations in the form of a "natural-parameter homotopy." This paper applies a homotopy method to track a continuous path of solutions, starting from a local supervised solution (\lambda = 0) to a local unsupervised solution (\lambda = 1). The homotopy method is guaranteed to track with probability one from \lambda = 0 to \lambda = 1 if the \lambda = 0 solution is unique; this condition is not satisfied for the HMM since the maximum likelihood supervised solution (\lambda = 0) is characterized by many local optima. A modified form of the homotopy map for HMMs assures a track from \lambda = 0 to \lambda = 1. Following this track leads to a formulation for selecting \lambda \in [0, 1) for a semisupervised solution and it also provides a tool for selection from among multiple local-optimal supervised solutions. The results of applying the proposed method to measured and synthetic sequential data verify its robustness and feasibility compared to the conventional EM approach for semisupervised HMM training.

Converting a biochemical reaction network to a set of kinetic rate equations is tedious and error prone. We describe known interface paradigms for inputing models of intracellular regulatory networks: graphical layout (diagrams), wizards, scripting languages, and direct entry of chemical equations. We present the JigCell Model Builder, which allows users to define models as a set of reaction equations using a spreadsheet (an example of direct entry of equations) and outputs model definitions in the Systems Biology Markup Language, Level 2. We present the results of two usability studies. The spreadsheet paradigm demonstrated its effectiveness in reducing the number of errors made by modelers when compared to hand conversion of a wiring diagram to differential equations. A comparison of representatives of the four interface paradigms for a simple model of the cell cycle was conducted which measured time, mouse clicks, and keystrokes to enter the model, and the number of screens needed to view the contents of the model. All four paradigms had similar data entry times. The spreadsheet and scripting language approaches require significantly fewer screens to view the models than do the wizard or graphical layout approaches.

This paper describes a new method to be used for matching three-dimensional objects with curved surfaces to two-dimensional perspective views. The method requires for each three-dimensional object a stored model consisting of a closed space curve representing some characteristic connected curved edges of the object. The input is a two-dimensional perspective projection of one of the stored models represented by an ordered sequence of points. The input is converted to a spline representation which is sampled at equal intervals to derive a curvature function. The Fourier transform of the curvature function is used to represent the shape. The actual matching is reduced to a minimization problem which is handled by the Levenberg-Marquardt algorithm [3].